Mathematics Commons^™

On Algebraic Aspects And Functoriality Of The Set Of Unbounded Operators Affiliated With A Von Neumann Algebra, Indrajit Ghosh

Doctoral Theses

In quantum theory, physically meaningful observables such as position and momentum are modeled by unbounded self-adjoint operators on Hilbert spaces. To study such operators in a rigorous mathematical framework, Murray and von Neumann introduced the concept of affiliation with a von Neumann algebra, giving rise to what are now known as Murray–von Neumann affiliated operators. For a single (unbounded) self-adjoint operator, its spectral projections span an abelian von Neumann algebra to which the operator is affiliated. If we want a common framework to study families of (unbounded) self-adjoint operators which do not necessarily commute with each other, it is instructive …

Topology Across Scales On Heterogeneous Cell Data, M. Torras-Pérez, Iris Yoon , '13, P. Weeratunga, L.-P. Ho, H. M. Byrne, U. Tillmann, H. A. Harrington

Mathematics & Statistics Faculty Works

Multiplexed imaging allows multiple cell types to be simultaneously visualised in a single tissue sample, generating unprecedented amounts of spatially-resolved, biological data. In topological data analysis, persistent homology provides multiscale descriptors of “shape" suitable for the analysis of such spatial data. Here we propose a novel visualisation of persistent homology (PH) and fine-tune vectorisations thereof (exploring the effect of different weightings for persistence images, a prominent vectorisation of PH). These approaches offer new biological interpretations and promising avenues for improving the analysis of complex spatial biological data especially in multiple cell type data. To illustrate our methods, we apply them …

Needs Analysis Of Interactive Learning Media For Teachingheat Transfer In Physics: Students’ And Teachers’Perspectives, Rizki Eka Shintya, Ika Mustika Sari, Ida Kaniawati

Jurnal Pendidikan Sains

Heat transfer material in physics is known to be abstract. This study specifically analyzes the conceptual difficulties, and visualization needs specific to this material, which is different from the analysis of physics needs in general. This analysis does not only look for the need for traditional media but explicitly looks for the need for interactive media (simulation, animation, virtual laboratory). Therefore, this study aims to identify the need for interactive learning media in physics education, specifically in the teaching of heat transfer, from the perspective of students and teachers in West Java, Indonesia. Using a quantitative descriptive survey, data were …

Efficacy Of Teaching At The Right Level Approach Combined With The Problem-Based Learning Model On Science Learning Outcomes At Middle School, Heri Syahputra Azhar Panjaitan, Ryan Dwi Puspita

Jurnal Pendidikan Sains

This research seeks to evaluate the efficacy of the Teaching at the Right Level (TaRL) strategy in conjunction with the Problem-Based Learning (PBL) model on the scientific learning outcomes of eighth-grade students at middle school Islam Terpadu Khairul Imam. This research addresses the inadequate scientific problem-solving abilities and science learning outcomes of Indonesian students, necessitating a more interactive and individualized instructional technique. The methodology used is a quasi-experimental design with a nonequivalent control group. The sample included two purposively chosen eighth-grade classes: one experimental class (n=25) underwent the TaRL–PBL intervention, whereas the control class (n=25) simply used the lecture approach. …

Second Moment Of Degree Three L-Functions, Sampurna Pal

Doctoral Theses

Let $F$ be a Hecke-Maa\ss\  cusp form for $SL(3,\mathbb{Z})$. In this dissertation, we obtain a non-trivial upper bound of the second moment of $L(F,s)$ in the $t$-aspect: $$ \int_{T}^{2T}|L(F,1/2+it)|^2 dt\ll_{F,\epsilon} T^{3/2-3/32+\epsilon}.$$ Immediate corollaries include improvements over the existing results on the Subconvexity bound for self-dual $GL(3)$ $L$-functions in the $t$-aspect and for self-dual $GL(3)\times GL(2)$ $L$-functions in the $GL(2)$ spectral aspect, the error term in the Rankin-Selberg problem, and the zero density estimate for $GL(3)$ $L$-functions.

Development Of Students Worksheet Based On Project-Based Learning To Train Critical Thinking Skills At Vocational High School, Dia Ayu Permatasari, Harun Nasruddin

Jurnal Pendidikan Sains

Critical thinking is a cognitive skill that helps identify problems and generate solutions, leading to logical decisions or considerations for solving those problems. Students' critical thinking skills can be trained through learning activities to further improve students' critical thinking skills with learning tools. Therefore, this research intends to produce a student worksheet based on project-based learning to train students' critical thinking skills on the colligative properties of solutions. The development research uses the 4D development model from Thiagarajan, limited to the development stage. A limited trial was conducted with 30 students of industrial chemical engineering expertise at Vocational High School …

Development Of Digital Comic Learning Media Based On Mobile Learning On Media: Making Media Materials In Plant Tissue Culture, Sufina Intan Pertiwi, Fauziyah Harahap, Aline Gusti Yolanda Harahap, Marsya Amira Indrawati, Aline Jelita Christiani Simanullang, Yanda Febry Gracea Br Tarigan, Maureen Efriyanti Sitinjak

Jurnal Pendidikan Sains

his research was conducted based on student needs analysis, analysis of learner characteristics, and curriculum analysis, namely the lack of visualization and presentation of concepts and the lack of utilization of interactive technology in the learning process on media material and media making in tissue culture for college students. This study intends to develop digital comic media based on mobile learning and making media materials in tissue culture. This research method used research and development (R&D) with the ADDIE model: analyze, design, develop, implement, and evaluate. The subjects of this study were students of the Department of Biology, Universitas Negeri …

Problem-Based Learning Assisted By Augmented Reality On The Respiratory System Topic: A Study Of Students’ Critical Thinking Skills And Learning Motivation, Nyimas Dilviana, Ade Yeti Nuryantini, Sumiyati Sa'adah

Jurnal Pendidikan Sains

This study aims to examine the effectiveness of the Problem-Based Learning (PBL) model assisted by Augmented Reality (AR) technology regarding the respiratory system in improving students’ critical thinking skills and learning motivation. The research method used was a quasi-experimental design with a one-group pretest-posttest model. The subjects were 30 eleventh-grade students from a public high school in Garut City. Research instruments included a critical thinking test and a learning motivation questionnaire. The results showed a significant improvement in students’ critical thinking scores after the implementation of PBL with AR support. Additionally, learning motivation data analyzed from 16 statement items revealed …

An Ode-Based Analytical Approach To Rayleigh Flow Of Kelvin–Voigt Fluid, Kamille Garcia, Mahanthesh Basavarajappa

CODEE Journal

We present some results from a project carried out in the Under- graduate Research in Mathematics (MATH 4380) course at TAMIU. The main goal of this study is to demonstrate that analytical solutions for a system of partial differential equations (PDEs) can be obtained using methods typically taught in an undergraduate ordinary differential equations (ODE) course, such as power series, undetermined coefficients, and Laplace transforms. In this study, we provide semi-analytical solutions for Rayleigh flow type problem utilizing the Kelvin-Voigt fluid model, which describes the behavior of vis- coelastic materials by incorporating both elastic and viscous properties. Heat transfer analysis …

A Bdg Inequality For Stochastic Volterra Integrals, Alexandre Pannier

Journal of Stochastic Analysis

We establish Burkholder-Davis-Gundy-type inequalities for stochastic Volterra integrals with a completely monotone convolution kernel, which may exhibit singular behaviour at the origin. When the supremum is taken over a finite interval, the upper bound depends linearly on the Lγ-norm of the kernel, for any γ > 2. We demonstrate the utility of this inequality in quantifying the pathwise distance between two stochastic Volterra equations with distinct kernels, with a particular emphasis on the multifactor Markovian approximation. For kernels that decay sufficiently fast, we derive an alternative inequality valid over an infinite time interval, providing uniformin- time bounds for mean-reverting stochastic Volterra …

Follow Me Into Math: Near-Peer Influencers Take The Stage, Aaron T. Wilson, Sergey Grigorian, Mayra Ortiz Galarza, Xiaohui Wang

School of Mathematical & Statistical Sciences Faculty Publications

Young people like to be entertained, and to entertain others. What if students were to invest enough of their time and effort into learning topics from our mathematics courses to become experts in the eyes of their peers? In this study we positioned college students and high school students as mathematical performers on the stage in front of their nearpeers, for whom they became math influencers, developing and presenting MathShows. The paper shows readers how we positioned students on the stage, using a 7-step MathShow Design Process informed by a Neer-peer Mathematical Mentoring framework. Of import for educators, researchers and …

Rogue Wave Patterns Associated With Adler–Moser Polynomials In The Nonlocal Nonlinear Schrödinger Equation, Tingyou Wang, Zhenyun Qin, Gui Mu, Fuzhuang Zheng, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, novel rogue wave patterns in the nonlocal nonlinear Schrödinger equation (NLS) are investigated by means of asymptotic analysis, including heart-pentagon, oval-triangle, and fan-triangle. It is demonstrated that when multiple free parameters get considerably large, rogue wave patterns can approximately be predicted by the root structures of Adler–Moser polynomials. These polynomials, which extend the Yablonskii–Vorob’ev polynomial hierarchy, exhibit richer geometric shapes in their root distributions. The (x,t)-plane is partitioned into three regions and through a combination of asymptotic results in different regions, unreported rogue wave patterns can be probed. Predicted solutions are compared with true rogue waves in …

Growth Mindset In The Mathematics Classroom: Studying The Effects Of A Growth Mindset Intervention On High School Students In A Geometry Classroom, Katelyn Strauss

Mathematics Graduate Theses

Having a growth mindset is crucial to being successful in a mathematics classroom. However, many students believe themselves to be either “mathematics people” or “not mathematics people”. When students believe they are not a mathematics person, they are far less likely to engage in material where they face struggles, and thus they miss out on valuable learning. A review of the literature has show that students have been able to shift their mindset from fixed to growth through a series of interventions. I used a unit in Geometry to see how a growth mindset intervention would affect the mindset of …

Dimension Of Subalgebras Of Fomin-Kirillov Algebras, Taro Ikeda, Sirous Homayouni

Annual Student Research Poster Session

One of the central open problems concerning the Fomin-Kirillov algebras was whether their dimension is finite or infinite. This question was recently resolved in one research by C. Barligea, where it was shown that FK(n) is infinite-dimensional for all n ≥ 6. In our work, we investigate the dimension of a certain subalgebra of FK(6).

(Si15-084) Application Of Differentiation Matrices Corresponding To Scaling And Wavelet Functions To Integral Equations, Viresh Kumar, Rakesh Kumar

Applications and Applied Mathematics: An International Journal (AAM)

In the present paper, we have studied the technique by which a differentiation matrix corresponding to scaling and wavelet function is helpful in representing an integral equation in discrete form. In this technique, only finite times continuously differentiable scaling and wavelet functions were used for the differentiation matrix. This method explores the applications of compactly supported wavelets in discretization of Fredholm integral equation and provides us with a bridge for the solution of integral equations via compactly supported finitely differentiable wavelets.

(Si15-017) Modeling Construction Project Uncertainty Using Fuzzy Inference And Nature-Inspired Metaheuristic Knowledge-Based Algorithms, M. Kapoor, B. K. Pathak, R. Kumar

Applications and Applied Mathematics: An International Journal (AAM)

Construction projects are influenced by various uncertain factors, including supervisory knowledge, labor expertise, and weather conditions. These uncertain factors have linguistic properties that are challenging to quantify with the help of traditional set theory. To address this, the study applies fuzzy inference systems, specifically the Mamdani fuzzy inference system, to model and evaluate the impact of these uncertainties on construction projects. This fuzzy inference system provides a more nuanced understanding of these factors compared to traditional set theory methods. Experimental results indicate that uncertainties significantly impact construction projects. These findings establish a valuable framework for developing adaptive strategies, enhancing project …

(Si15-140) Designing Bayesian Double Sampling Plans Based On Zero Inflated Poisson Distribution, Priyadharshini R., Shalini K., Hemalatha R., Sangeetha S.

Applications and Applied Mathematics: An International Journal (AAM)

The implementation of attribute-based sampling inspection serves as a quality control technique used across numerous industries to evaluate items or workflow processes. When the data exhibits a substantial number of zero counts, the zero-inflated Poisson (ZIP) distribution serves as an effective model for accommodating this zero-inflation. Double sampling plan (DSP) is a quality check method where the decision to approve or decline a batch comes after examining two samples, providing more conclusive information compared to a single sample plan (SSP). In practice, effective decision-making regarding submitted lots considers both within-lot and between-lot variations, which can be addressed through the use …

(Si15-142) Selection Of Single Sampling Plans Based On Zero Inflated Binomial Distribution Using Cost Optimization, Sangeetha S., Shalini K., Hemalatha R., Priyadharshini R.

Applications and Applied Mathematics: An International Journal (AAM)

Economic design of sampling plans involves creating sampling plans that minimize the total cost associated with the inspection process while ensuring quality. It aims to address the quality risk concerns of both producer and consumer, ensuring product quality while minimizing inspection costs. This article’s objective is to design single sampling plans by attributes based on Zero-inflated Binomial (ZIB) distribution, using cost optimization principles by developing an economic model aimed at achieving optimal total cost by considering the Average Total Inspection (ATI). Numerical illustration is provided to illustrate the selection of single sampling plans under ZIB distribution that minimizes producer’s total …

(Si15-067) Ahp And Moora Decision Making Methods On Bipolar Fuzzy Sets, S. Anita Shanthi, R. Preethi

Applications and Applied Mathematics: An International Journal (AAM)

Decision making, in the present contemporary world, has been inherently complicated. Nowadays, the major challenge is the selection of an appropriate option. The arrival of numerous brands and models makes a purchase challenging. Hence, in this paper, four different models of the same branded laptops are considered, for the selection of an appropriate option, using the Analytic Hierarchy Process (AHP) and Multi-Objective Optimization on the basis of Ratio Analysis (MOORA), with bipolar fuzzy sets, which help decision makers arrive at the most logical choice based on their preferences. The bipolar fuzzy Analytic Hierarchy Process efficaciously supports decision making in cases …

(Si15-022) Five Efficient Cryptography Authentication Schemes With Functional Relation On General Spaces, L. Sreenivasulu Reddy, S. Lakshmisri

Applications and Applied Mathematics: An International Journal (AAM)

This work addresses the growing demand for diversification in cryptographic schemes to secure communication. This work proposes a novel suite of algorithms, including two block ciphers (TPBlock and TAP-Block), two stream ciphers (TP-Stream and TAP-Stream), and a zero-knowledge proof scheme (F-zero knowledge proof). All schemes leverage functional relations defined over the real number space with a dimension greater than one for encryption, decryption, and key generation, offering an alternative to the number-theoretical aspects and algebraic structures commonly used in existing schemes. The main goal of this work is to introduce and propose these five novel cryptographic schemes to provide authentication …

(Si15-010) On Perturbations Of Gabor Frames, Jamkhongam Touthang

Applications and Applied Mathematics: An International Journal (AAM)

Stability plays a crucial role in frame theory and its applications. The present paper studies the interaction between Gabor frames and perturbations, presenting perturbation results related to small changes of the frame parameters and the window functions both in regular and irregular settings. Examples are provided for illustration. Additionally, the paper briefly discusses algorithms pertinent to Gabor frames under perturbations and highlights challenging areas in the field.

(Si15-064) Permutation Pentanomials Over Finite Fields With Even Characteristic, Shalini Gupta, Sushil Kumar, Ashima .

Applications and Applied Mathematics: An International Journal (AAM)

Permutation polynomials over finite fields constitute an active area of research and play an important role in diverse domains, including finite geometry, combinatorial design, coding theory, and cryptography. The study of these polynomials has a long history, and many results have been obtained in recent years. This paper presents new classes of permutation pentanomials based on permutation over the unit circle of finite fields with even characteristic that contribute to the theoretical development of permutation polynomials.

(Si15-120) Exploring Fractional Difference Equations And Their Applications With Mahgoub-Transform, Tharmalingam Gunasekar, Periyasamy Udhayasankar, Prabakaran Raghavendran, Kamalendra Kumar

Applications and Applied Mathematics: An International Journal (AAM)

We discuss the introduction and study of the nabla discrete Mahgoub transform along with its defining properties. The transform of fractional sums and fractional differences are derived, demonstrating the applicability of the transform from the computational viewpoint. Employing the transform, fractional difference equations with initial value problems are solved, thereby enhancing the knowledge of their closed forms. As a side-effect of the Mahgoub-transforms, an attractive connection is established, showing that the discrete Mittag-Leffler function acts as the eigenfunction for the Caputo-type fractional difference operator nabla. These results strengthen the core basis for fractional calculus and herald industrial applications in various …

Coefficients Of The Characteristic Polynomial Of A Hypergraph And Their Combinatorial Properties, Utku Okur

Theses and Dissertations

We investigate the combinatorial properties of the characteristic polynomial $\phi_\mathcal{H}\ev{t}$ of a hypergraph $\mathcal{H}$, in particular, its coefficients. Due to a classical result of Jacobi, the generating function of closed walks at a vertex $u$ in a graph $G$ is determined by the rational function $\phi_{G-u}(t) / \phi_G(t)$. The connection between closed walks of $G$ and its characteristic polynomial has a known elegant proof via an application of Viennot's Heaps of Pieces framework, where cycles are taken as pieces and the concurrence relation is sharing a vertex. Here, we prove a bijection between heaps with a unique maximal piece containing …

Investigating The Influence Of Instructional Strategies On The Development Of Procedural And Conceptual Knowledge In Advanced Algebra Ii Students, Maura Frances Yinger

Theses and Dissertations

This mixed-methods action research study investigated the influence of instructional strategies shown to improve students’ procedural and conceptual understanding in a rational expressions and equations unit in Advanced Algebra II. The instructional strategies used in the study include comparing, self-explaining, and exploring before instruction. The students (N=27) completed a pre-test and a post-test, both of which were followed by questions asking students to justify their responses on two questions. All students also responded to six digital self-explanation journal prompts. Randomly selected students were placed into three homogenous groups to participate in performance task observations. Analysis of the data …

Art Forms: Born Out Of Necessity, Urmi Duttagupta

Publications and Research

This collection of artworks expresses the artist’s profound passion for mathematics and life’s complex balance. As a female mathematician, she uses artistic expression and intricate patterns to evoke mathematical beauty and feminine strength, celebrating the presence and resilience of women in mathematics.

Memoir On A General Property Of A Very Extensive Class Of Transcendental Functions, Niels Henrik Abel 1802--1829, John Little

Mathematics and Computer Science Department Faculty Scholarship

We present this new commentary and translation anticipating the 200th anniversary of the work, commonly known as Abel's ``Paris memoir.'' This is recognized today as one of Abel's most original and influential works. It is significant mostly because it marked the first appearance of a form of a result in the theory of algebraic curves and Riemann surfaces that has come to be known as ``Abel's theorem.'' However, Abel's original understanding of the meaning and context of his result was quite different from the typical modern formulation and the development of the modern understanding has been a long and tortuous …

Packing Independent Cliques Into Planar Graphs, Csaba Biró, Gabriel Collado, Oscar Zamora

Theory & Applications of Graphs

The indeque number of a graph is largest set of vertices that induce an independent set of cliques. We study the extremal value of this parameter for the class and subclasses of planar graphs, most notably for forests and graphs of pathwidth at most $2$.

The Calvin University Math Department History 1920-2020, Michael Stob

University Histories

No abstract provided.

Energy Statistic-Based Goodness-Of-Fit Test For The Lindley Distribution With Application To Lifetime Data, Joseph Njuki, Ryan Avallone

Mathematics and Statistics

In this article, we propose a goodness-of-fit test for a one-parameter Lindley distribution based on energy statistics. The Lindley distribution has been widely used in reliability studies and survival analysis, especially in applied sciences. The proposed test procedure is simple and more powerful against general alternatives. Under different settings, Monte Carlo simulations show that the proposed test is able to be well controlled for any given nominal levels. In terms of power, the proposed test outperforms other existing similar methods in different settings. We then apply the proposed test to real-life datasets to demonstrate its competitiveness and usefulness.

This article …